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Constraints on the reheating temperature from sizable tensor modes

Despite its importance for modeling the homogeneous hot early universe very little is experimentally known about the magnitude of the reheating temperature, leaving an uncertainty of remarkable 18 orders of magnitude. In this paper we consider a general class of polynomial inflaton potentials up to fourth order. Employing a Monte Carlo scan and imposing theoretical and experimental constraints we derive a robust lower limit on the energy scale at the end of inflation, $V_\text{end}^{1/4} > 3 \times 10^{15}$ GeV for sizable tensor modes, $r \geq 10^{-3}$. If the reheating phase is perturbative and matter dominated, this translates into a lower bound on the reheating temperature, yielding $T_\text{rh} > 3 \times 10^8 \; (7 \times 10^2)$ GeV for gravitational inflaton decay through a generic dimension five (six) operator.